I do something very similar with AWS SSM and it works without issue:

db_uri = pulumi.Output.all(
            username=self.database.username,
            password=self.database.password,
            endpoint=self.database.endpoint,
            db_name=self.database.db_name,
        ).apply(
            lambda args: f"postgresql://{args['username']}:{args['password']}@{args['endpoint']}/{args['db_name']}",
        )
        self.db_uri = aws.ssm.Parameter(
            f"{name}-db-uri",
            type="SecureString",
            value=db_uri,
            tags=args.tags,
            opts=pulumi.ResourceOptions(parent=self),
        )